This invention relates to a much more efficient method and apparatus to reduce the drag of plates or vessels moving relative to a fluid and of internal flows such as liquids moving through marine water-jet propulsors. The invention can be used to eject additives into specific regions of the boundary layer to modify the rheological properties of the fluid without the undesirable disruption of the boundary layer and without the rapid diffusion of the additive across the boundary layer inherent in traditional ejection techniques.
In the past, the effectiveness and efficiency of drag reduction obtained by ejecting non-Newtonian additives in xe2x80x9cexternalxe2x80x9d turbulent boundary layer flows has been limited relative to the effectiveness and efficiency observed in xe2x80x9cinternalxe2x80x9d or pipe flows. In high Reynolds number turbulent pipe flows, reductions in friction drag of 70 to 80 percent are observed, while for ejection into high Reynolds number turbulent flows over a flat-plate, the maximum observed reduction in friction drag has been only about 40 to 60 percent. Further, the high additive expenditure rates experienced for external boundary layers have limited the economic benefit of implementing additive systems on maritime transport craft. Ejection techniques to introduce additives into external flows also have introduced unsteadiness and, in some cases, unfavorable viscosity gradients into the boundary layer, such that the penalties associated with the ejection process resulted in a greatly reduced net benefit. A more efficient method for introducing additives into the near-wall region of the boundary layer for drag reduction is needed.
In the prior art, advances were directed toward additive mixing or bubble generation and little attention was given to the ejector itself. U.S. Pat. No. 4,186,679 to Fabula et al (which issued Feb. 5, 1980), is representative of the modest attention paid to the ejector system itself. In this case, the ejector is identified as xe2x80x9ca plurality of rearwardly raked ejection apertures.xe2x80x9d Similarly, in U.S. Pat. No. 4,987,844 to Nadolink (which issued Jan. 29, 1991), the focus is on methods and apparatus to pump solvent passively, to mix multiple additives or suspensions, and to direct the mixture to the location of minimum pressure coefficient for ejection. The ejection apparatus is only identified as being one of many options, specifically xe2x80x9ceither screening, mesh, a porous media, perforated material, drilled holes of specific geometry, a circumferential slot, etc., xe2x80x9d and that xe2x80x9cother forms of ejection apparatus . . . may be employed to achieve the result of the present invention.xe2x80x9d In U.S. Pat. No. 5,445,095, by Reed et al (which issued Aug. 29, 1995), longitudinal riblets are combined with polymer ejection to predictably control the rate of diffusion of the polymer. However, the maximum downstream distance at which the material has completely diffused away from the riblets was identified as about 400 riblet widths, which scales to the order of centimeters for a marine vehicle, while the diffusion distance for the present invention has been shown to be on the order of tens of meters. As with the other inventions, no specific ejection technique is identified; only a series of xe2x80x9cfeasiblexe2x80x9d methods are listed. In Japanese Laid Open Patent Applications 09 151913 and 09 151914 by Mitsutake Hideo and Yoshida Yuki, respectively, both published 29-11-95, air bubbles are distributed along the submerged surface of a ship to reduce drag. In the first laid open patent application the ejectors are simply straight tubes, one for air bubbles and one upstream for a liquid. The purported purpose of the upstream xe2x80x9chigh kinetic energyxe2x80x9d ejector is to entrain the air bubbles from the downstream ejector on the inside of the boundary layer near the submerged surface. The second laid open patent application is entitled xe2x80x9cMicrobubble Generatorxe2x80x9d, but a key component is a backwards (upstream) slanting flexible bubble generator with a sinusoidal fluid path. The ejection port is the outlet of the bubble generator, which faces upstream against the flow. The effects with regard to ejecting additives against the flow or disrupting the established boundary layer with a high-energy wall jet are not addressed.
A classical discussion of boundary layer theory, including formulation of Navier-Stokes and turbulent boundary layer equations, is provided in Boundary-Layer Theory, by Dr. Hermann Schlichting, published by McGraw Hill, New York, seventh edition, 1979. A discussion of structures and scales in turbulent flows can be found in Turbulence, 1975, McGraw Hill, written by J. O. Hinze, and in xe2x80x9cCoherent Motions in the Turbulent Boundary Layer,xe2x80x9d in Annual Review of Fluid Mechanics, 1991, Volume 23, pp. 601 to 639, written by Steven K. Robinson. The potential of dilute aqueous solutions of long-chain polymer molecules to reduce drag, now known as the Toms"" Effect, was introduced by B. A. Toms at the First International Congress on Rheology in Amsterdam in 1948 and was published in the proceedings of that conference. P. S. Virk et al introduced the concept of drag reduction limits with polymer solutions in turbulent pipe flows in a paper entitled, xe2x80x9cThe Ultimate Asymptote and Mean Flow Structures in Toms"" Phenomenon,xe2x80x9d published in the ASME Journal of Applied Mechanics, 37, pages 488 to 493, in 1970. Virk et al related the level of drag reduction to an increase in the thickness of the buffer zone which, in turn, was limited by the pipe diameter. For external flows, no such physical constraint is imposed. However, D. T. Walker, his professor W. G. Tiederman, and colleague T. S. Luchik, in a paper entitled, xe2x80x9cOptimization of the ejection process for drag-reducing additives,xe2x80x9d which was published in Experiments in Fluids, 4, pages 114 to 120, in 1986, obtained drag reduction limits for slot ejection in a channel flow were 20 to 40 percent less than the maximum drag reduction observed in pipe flows. These observations were confirmed by others, such as Yu. F. Ivanyuta and A. A. Khomyakov in their article on the xe2x80x9cInvestigation of Drag Reduction Effectiveness with Ejection of Viscoelastic Polymer Solutions,xe2x80x9d which was published in the Proceedings of the International Shipbuilding Conference, KRSI, October, 1994, St. Petersburg, pages 163 to 170, in Russian.
While dilute solutions of polymer behave as Newtonian fluids in laminar flows, A. Gyr and H. W. Bewersdorff, in their text, Drag Reduction of Turbulent Flows by Additives, Kluwer Academic Publishers, 1995, point out that in certain laminar flows, such as laminar contraction flows, polymer solutions exhibit non-Newtonian behavior. The hypothesis cited is that in such a flow, as in turbulent flow, the long molecules of the additive become stretched (uncoiled and elongated) and aligned in the flow which are necessary conditions for the solution to exhibit non-Newtonian behavior. V. G. Pogrebnyak, Y. F. lvanyuta, and S. Y. Frenbel, in their paper, xe2x80x9cThe Structure of the Hydrodynamic Field and Directions of the Molecular Slope of Flexible Polymers Under Free-Converging Flow Conditionsxe2x80x9d published in Russian in Polymer Science USSR. Vol. 34, No. 3, 1992, define the conditions under which the polymer molecules can be uncoiled, aligned, and sufficiently stretched to become effective in drag reduction.
Experiments by C. S. Wells and J. G. Spangler, described in their paper, xe2x80x9cInjection of a Drag-reducing Fluid into Turbulent Pipe Flow of a Newtonian Fluidxe2x80x9d published in The Physics of Fluids, Vol. 10, No. 9, pages 1890 to 1894, September, 1967, by M. M. Reischman and W. G. Tiederman described in an article, xe2x80x9cLaser-Doppler Anemometer Measurements in Drag-reducing Channel Flows,xe2x80x9d published in the Journal of Fluid Mechanics, Vol. 70, Part 2, pages 360 to 392, in 1975, and by W. D. McCombs and L. H. Rabie in xe2x80x9cLocal Drag Reduction Due to Injection of Polymer Solutions into Turbulent Flow in a Pipe,xe2x80x9d Parts I and II, published in the AlChE Journal, Vol. 28, No. 4, pages 547 to 565, in July 1982, have clearly demonstrated that polymer additives can reduce drag when they are in the near-wall region of the turbulent boundary layer, known as the buffer zone. In viscous wall units, hereinafter termed y+, which are length values non-dimensionalized with friction velocity and kinematic viscosity, the region was between about 20 and 100 viscous wall units from the wall. It has been noted that at high levels of drag reduction, the buffer zone is thickened and can extend out to several hundred viscous wall units. No drag reduction or related effects were observed when polymer was confined to the region where viscous shear stresses dominate over Reynolds stresses, that is, inside of about 12 viscous wall units. The convention used in the literature is a y+value of 11.6. As shown by many, including A. A. Fontaine, H. L. Petrie, and T. A. Brungart in their paper xe2x80x9cVelocity Profile Statistics in a Turbulent Boundary Layer with Soft-Injected Polymer,xe2x80x9d published in the J. Fluid Mechanics, Vol. 238, pages 435 to 466 in 1992, the flow through this region per unit span, Qs, is equal to 67.3 times the kinematic viscosity of the fluid. For a given fluid and fluid temperature, this flow rate is independent of freestream velocity and distance from the beginning of the boundary layer.
While the sensitivity of drag reduction to additive location within the boundary layer has been recognized since 1967, the elegant work of M. Poreh and J. E. Cermak regarding the xe2x80x9cStudy of Diffusion from a Line Source into a Turbulent Boundary Layer,xe2x80x9d published in the Int. Journal Heat and Mass Transfer, No. 7, in 1964, convinced most researchers that diffusion of the ejected fluid was inevitable and rapid. Thus, as reported by J. W. Hoyt and A. G. Fabula xe2x80x9cFrictional Resistance in Towing Tanks,xe2x80x9d published in the Proceedings of 10th Industrial Towing Tank Conference, at Teddington England, in 1963, by T Kowalski on xe2x80x9cThe Effect in Resistance of Polymer Additives Injected into the Boundary Layer of a Frigate Model,xe2x80x9d published in the Transactions of the Eleventh International Towing Tanks Conference of Ship Tank Superintendent, at Tokyo, in 1966, by H. L. Dove and H. J. S Canham on the HMS Highburton Speed Trials with Polyox Injection into the Boundary Layer, published in AEW Report No 11/69, by, W. Xiliang, D. Yongxuan, X. Changsheng, and W. Guigin in xe2x80x9cDrag Reduction by Polymer Ejection Described,xe2x80x9d published in Shipbuilding of China, No. 66, page 45 to 57 in July, 1980, and by researchers in the Soviet Union as described by B. F. Dronov and B. A. Barbanel in their paper xe2x80x9cEarly Experience of BLC Techniques Usage in Underwater Shipbuilding,xe2x80x9d published in the Proceedings of Warship 99. Naval Submarine 6, by the Royal Institute of Naval Architects, London in June, 1999, the investigators used a wide array of angled slots or circular apertures to eject sufficient material to flood the entire boundary layer. Because of the acceptance of rapid diffusion, not only through but even outside the boundary layer, the amount of material ejected was often several times that calculated to flood the entire boundary layer at its greatest extent. Ejection velocities were usually of the same order as the free-stream velocity and ejected mass flow rates often exceeded 100 Qs.
In the paper, xe2x80x9cSuppressed Diffusion of Drag-reducing Polymer in a Turbulent Boundary Layer,xe2x80x9d published in the Journal of Hydronautics, No. 6 in 1972, J. Wu, and then D. Collins in his thesis entitled, xe2x80x9cA Turbulent Boundary Layer with Slot Injection of Drag-reducing Polymer,xe2x80x9d at the Georgia Institute of Technology in July, 1973, first reported a lower diffusion rate for polymer solutions than was generally accepted. In 1989, D. T. Walker and W. G. Tiederman confirmed those observations in their papers xe2x80x9cSimultaneous Laser Velocimeter and Concentration Measurements,xe2x80x9d published in the Journal of Laser Applications 1, pages 44 to 48 in 1989, and xe2x80x9cThe Concentration Field in a Turbulent Channel Flow with Polymer Injection at the Wall,xe2x80x9d published in Experiments in Fluids, 8, pages 86 to 94 in 1989. In the early 1990s there was growing recognition that the Poreh and Cermak work, held as the standard for diffusion behavior, could be applied only to the introduction of xe2x80x9cpassivexe2x80x9d contaminants into the turbulent flows. Specifically, xe2x80x9cactivexe2x80x9d contaminants, such as aqueous solutions of high molecular weight polymers, that affect the character of turbulence and, hence, the process of diffusion, do not behave the same: diffusion can be more gradual. This was confirmed by T. A. Brungart, L. L. Petrie, W. L. Harbison, and C. L. Merkle in their work using xe2x80x9cA Fluorescence Technique for Measurement of Slot-injected Fluid Concentration Profiles in a Turbulent Boundary Layer,xe2x80x9d and published in Experiments in Fluids, 11, in 1991. The next year S. T. Sommer and H. L. Petrie published xe2x80x9cDiffusion of slot-injected drag-reducing polymer solution in a LEBU-modified turbulent boundary layerxe2x80x9d in Experiments in Fluids, 12, in which they demonstrated, in relatively high-speed flows, that control or modification of the outer flow field at the ejection slot with a pair of large-eddy break-up devices (LEBUs), further reduced the rate of polymer diffusion across the boundary layer. Further, A. A. Fontaine, H. L. Petrie, and T. A. Brungart in their paper, xe2x80x9cVelocity Profile Statistics in a Turbulent Boundary Layer with Slot-injected Polymer,xe2x80x9d published in the Journal of Fluid Mechanics, 238, pages 435 to 466 in 1992, showed that a reduction in the mass flow rate of the ejected fluid by a factor of two and a doubling of the concentrations to maintain a constant polymer expenditure rate produced a further reduction in the diffusion rate.
W. B. Amfilokhiev, B. A. Barbarnel, and N. P. Mazaeva in their paper on xe2x80x9cThe Boundary Layer with Slot Injection of Polymer Solutions,xe2x80x9d prepared for the Tenth European Drag Reduction Working Meeting, Mar. 16 to 17, 1997, point out that experience had demonstrated that a single slot with very high concentration was superior to the same amount or more additive being ejected from multiple slots along the length of the vessel. This empirically based insight was validated by Tiederman, Luchik, and Bogard in their work represented in xe2x80x9cWall-Layer Structure and Drag Reduction,xe2x80x9d published in the Journal of Fluid Mechanics, Vol. 156, page 419 to 437 (1985), where they showed that ejection at even modest discharge rates was disruptive to the boundary layer and resulted in an increase in the local skin friction drag, upstream, at, and just downstream of the ejection site. W. M. Kays and M. E. Crawford in their text on Convective Heat and Mass Transfer, published by McGraw-Hill, Inc. (1993), third edition, pages 226 to 230, point out that when the ratio of the mass flux of a second or ejected fluid normal to the mass flux of the freestream or first fluid exceeds 0.01, the boundary layer xe2x80x9cis literally blown off the wall surface.xe2x80x9d
A good summary of their own research, as well as the research of other experimenters with gas injection, is presented by C. L. Merkle and S. Deutsch in their article, xe2x80x9cDrag Reduction in Liquid boundary Layers by Gas Injection.xe2x80x9d The article is included in the text, Viscous Drag Reduction in Boundary Layers, edited by D. M. Bushnell and J. N. Hefner, Vol. 123, pages 351 to 410, and was published in 1990.
Allowed U.S. patent application Ser. No. 09/223,783 entitled xe2x80x9cMethod for Reducing Dissipation Rate of Fluid Ejected Into a Boundary Layerxe2x80x9d, which was filed on Dec. 31, 1998, and which issued as U.S. Pat. No. 6,138,704, describes a method to introduce ordered vorticity upstream of and in the ejected drag-reducing fluids. Controlled and favorable vorticity is employed to keep the ejected fluid in the near-wall region and to orient the molecules or structures of the additive in the configuration in which they are most effective.
A discussion and experimental results of providing a positive or favorable viscosity gradient in the near-wall region of the boundary layer is available in the paper by J. Kato, Y. Fujii, H. Yamaguchi, and M. Miyanaga entitled, xe2x80x9cFrictional Drag Reduction by Injecting High-viscosity Fluid into a Turbulent Boundary Layer,xe2x80x9d published in Transactions of the ASME, 115, pages 206 to 211, in June, 1993. The adverse effect of producing a negative viscosity gradient when ejecting polymer was identified in the previously identified paper by C. S. Well and J. G. Spangler (1967) and in papers by J. Wu and M. Tulin, such as xe2x80x9cDrag Reduction by Ejecting Additive Solutions into a Pure Water Boundary Layer,xe2x80x9d which was published in the Transactions of the ASME, Journal of Basic Engineering, in 1972. In their previously cited 1994 paper (in Russian), Yu. F. Ivanyuta and A. A. Khomyakov present a theoretical argument that a positive viscosity gradient will promote stabilization in laminar flow. They then present results from a series of experiments in turbulent flow in which they purport to establish a favorable viscosity gradient by using a special ejector. No geometry of the ejection system and no details of the method to achieve the favorable viscosity gradient were presented, but the plotted results indicated that the reduction in towed resistance was increased from about 50 percent to about 70 percent on their very long (40 m), but small-diameter (0.4 m), body. They also reported that their measurements of local drag reduction indicated a constant improvement (greater drag reduction), relative to their previous ejection method, along the length of the towed body.
Quite separate from using additives for boundary layer control, there are techniques to retard or eliminate flow separation which otherwise would lead to increased drag. F. 0. Ringleb described the potential for xe2x80x9cSeparation Control by Trapped Vorticesxe2x80x9d in the text Boundary Layer Control, Vol. 1, G. V. Lachmann, editor, published by Pergamon Press in 1961, as well as in a xe2x80x9cDiscussion of Problems Associated with Standing Vortices and their Applications,xe2x80x9d presented at the ASME Symposium on Fully Separate Flows in Philadelphia, Pa. on May 18 to 20, 1964. The concept is to provide an abrupt change in configuration geometry in a region where the flow path is otherwise continuous, but where separation would be expected on the continuous surface or wall. An abrupt change in geometry, such as produced by a transverse groove, can produce a strong vortex in the groove. Thus, the attached flow above the vortices bridges over the groove and remains attached downstream. This technique of producing stable entrained vorticity has been used to avoid or reduce an extended wake of separated flow. Sometimes referred to as Ringleb vortices, they are often used in diffusers and at the base of blunt bodies.
Discussions of wall jets to control separation of incompressible turbulent flow can be found in Control of Flow Separation by Paul K. Chang, published by Hemisphere Publishing Corporation, in 1976. Jets of the same fluid as in the freestream are used to entrain the freestream flow in regions of an adverse pressure gradient. The concept is to use the excess momentum of the wall jet to offset the loss of boundary layer momentum resulting from skin friction. However, without a careful balance of the two effects, the benefit can be diminished or even reversed by the increase in wall shear stress produced by the jet. Mixing is enhanced because of the unsteadiness introduced into the boundary layer by the jet. A. I. Tcygan""uk, L. F. Koziov, V. N. Vovk, and S. L. Maximov described a method and device to reduce the unsteadiness introduced by a wall jet in their invention entitled, xe2x80x9cTechnique for Control of the Near-wall Layer Flowing Over a Hard Body by the Method of a Control Jet and a Device for Realization of this Technique,xe2x80x9d which was published in Bulletin #30 of Aug. 15, 1990, as Soviet Inventor""s Certificate Number S.U. 1585569 A1. This method and device differ from other wall jet systems intended to entrain the boundary layer because of the creation of a vortex zone in the region where the control jet joins the freestream flow. The invention claims the vortex zone is produced by a vortex chamber when it has an opening to the jet that is approximately 0.28 of the length of the chamber.
The present invention enables the non-disruptive ejection of fluids into selected strata of the near-wall region of the boundary layer of a fluid flow. As its first objective, the present invention preconditions the upstream flow to reduce the initial diffusion of additive when it merges with the boundary layer flow. The second object of the invention is to precondition the ejected stream and the additive within the ejected stream such that it is immediately effective in reducing turbulent diffusion and the loss of momentum within the ejected fluid as it enters the boundary layer. A third object of the invention is to inhibit undesirable disruption of the established flow field. A fourth object of the invention is to eliminate the unfavorable viscosity gradient inherent in the ejection of high concentrations of a non-Newtonian additive or gas-liquid mixture; the fifth object of the invention is to allow the selective placement of multiple additives in strata across the boundary layer; the sixth object is to place additive or flow structure at specific locations above the near-wall flow to shield the near-wall flow, thereby further reducing the diffusion of ejected additives. The seventh object of the invention is to permit multiple ejector sets to be located along the length of the plate or vessel to maintain an optimum concentration of material, thereby enhancing overall system efficiency.
The boundary layer control system of the present invention includes pre-ejection processes, ejection processes, and post-ejection processes. The pre-ejection processes relate to conditioning the upstream flow to reduce the level of initial diffusion before the additive can take full effect. The ejection processes include conditioning of and directing the ejected fluid to accelerate the effect of the additive in reducing the turbulent diffusion at the ejector and inhibit the introduction of unsteadiness into the boundary layer, both upstream and downstream of the ejection point. The mass flow rate of the ejected fluid is selected based on the near-wall flow parameters of the established boundary layer in order to avoid an undesirable increase in the level of turbulence.
Since the ejection process is much less disruptive, multiple ejection locations can be implemented simultaneously without the penalties observed with traditional additive ejection techniques. Further, individual ejectors can be placed immediately adjacent to each other to allow ejection of multiple additives into selected strata of the downstream boundary layer, thereby providing for the control of rheological characteristics of the boundary layer, such as establishing and maintaining a favorable viscosity gradient after ejection. The ejection apparatus comprises a unique arrangement of fluidics devices including transverse grooves, vortex chambers, Coanda surfaces, internal nozzles, and knife-edges.
As used herein a xe2x80x9cCoandaxe2x80x9d surface refers to a convex-shaped, curved surface which produces a Coanda effect on a stream of flowing liquid. The Coanda effect refers to a wellknown fluid-dynamic phenomenon whereby a fluid with momentum due to its velocity will follow a curved surface contour, approximately as would an inviscid fluid. This flow will be maintained as long as a balance exists between the pressure gradient normal to the surface and a force, commonly termed xe2x80x9ccentrifugal forcexe2x80x9d, resulting from flow of the fluid around the convex-shaped, curved surface. The balance between these two forces is normally destroyed by the thickening of the boundary layer and the dynamic pressure of the free stream. Thus, a surface that is specially designed to have its convex curvature vary according to well-known criteria so as to produce a Coanda effect on an adjacent flowing fluid is hereinafter termed a xe2x80x9cCoanda surfacexe2x80x9d.
The present invention is different from all previous additive ejectors in that it substantially reduces the vorticity introduced on the upstream and downstream edge of the ejector. It conditions the upstream flow to reduce the level of turbulence and, hence, diffusion at the ejector. It preconditions the additive so that it is unwound, aligned, and stretched before merging with the external boundary layer flow. And, it conditions the downstream flow by keeping bubbles off the wall and establishing a favorable viscosity gradient at the wall immediately downstream of the polymer ejector. No ejection system of the prior art enables the non-disruptive placement of multiple additives in specific strata of the near-wall region of the boundary layer, as in the present invention.